Answers:
minor arc RP = 125 degrees
minor arc QS = 125 degrees
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Explanation
Definition: A minor arc is a piece of a circle such that it is smaller than a semi-circle with the same radius. In other words, it's measure is always less than 180 degrees.
Based on this definition, a minor arc is where we take the shortest path between any two points on a circle. For minor arc RP, we start at R then go to the right and take the shortest path to P. We do not go left when we start at R because that's the longer path and it is the major arc.
Minor arc RP is subtended by central angle ROP = 120 degrees. This central angle is equal to the arc measure in question. This isn't really a theorem, but more a definition if anything.
Central angle QOS is equal to angle ROP through the vertical angles theorem. Any pair of vertical angles are always congruent. Since QOS is 125 degrees, so is minor arc QS.
11: 4d to the second power
12: 16y to the seventh
13: a to the second, c to the second, d to the second
14: 12a to the forth, b
15: 20 a to the third,b to the second, c to the third, d
16:6 a to the second power, b, c, d
Answer:
5π, about 15.708 units
Step-by-step explanation:
A 3-4-5 triangle is a right triangle. When a circle circumscribes a right triangle, the hypotenuse is the diameter of the circle. The circumference of a circle is given by ...
C = πd
For a diameter of 5 units, the circumference is ...
C = π(5) = 5π = 15.708 . . . units
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<em>Additional comment</em>
The (3, 4, 5) triple is one of the first Pythagorean triples you run across. It is the smallest integer triple, and the only primitive triple with values in an arithmetic sequence. You can show this is a Pythagorean triple by ...
3² + 4² = 9 +16 = 25 = 5²
That is, these numbers satisfy the Pythagorean theorem relation for sides of a right triangle.
Answer:
See below.
Step-by-step explanation:
1.) 5√6
2.) 6√2
3.) 3√7
To solve this without the use of a calculator, split the given number into a series of products (numbers multiplied) and look for pairs.
Look at the attached example of Problem 1 to get a better idea of what I mean.
Answer:
With wind = 1000 km /hr
In calm air = 800 km/hr
Step-by-step explanation:
With wind :
Distance traveled = 1500 km
Time taken = 1.5 hours
Speed of plane in air :
Speed = distance / time
Speed = 1500 km / 1.5 hours
Speed = 100 km pe hour
In calm air :
Time taken = 1.875 hours
Distance = 1500 km
Speed of wind in calm air :
Distance / time
1500 km / 1.875
= 800 km/hr
